Said usually when at a loss for words to describe the sighting of a black person (usually male) who possesses indescribably awesome attributes or qualities such as wearing a cool hat, keepin' a ho in line, beatin' down the white oppressors or just generally being ghetto and black.
Some popular Righteous Nigs include -
Samuel L Jackson
Laurence Fishburne
Tupac
Snoop
Dre
That Black Guy That Plays Drums For Jason Mraz